Sentence examples for identity element for from inspiring English sources

An element has finite order if its product with itself eventually produces the identity element for the group.

There must also be a zero (which functions as an identity element for addition), negatives of all elements (so that adding a number and its negative produces the ring's zero element), and two distributive laws relating addition and multiplication [a(b + c) = ab + ac and (a + b c = ac + bc for any a, b, c].

For instance, if R = L K ( 1, n ), then R ⊕ R n - 1 = R n ≅ R. Using this, it's trivial to conclude that [ R n - 1 ] is an identity element for V ( R ) { [ 0 ] } = { [ R ], [ R 2 ], ⋯, [ R n - 1 ] }.

The gap type conjectures can be formulated for other asymptotic characteristics of groups like return probabilities (P^{(n)}_{e,e}) ((e) denotes the identity element) for a non degenerate random walk on a group, Fölner function (mathcal F (n),) or spectral density (mathcal N (lambda ).) There is a close relation between them and the Gap Conjecture on growth, which was mentioned in [22].

When adding zero to any number, the quantity does not change; zero is the identity element for addition, also known as the additive identity.

As a result of this identity, the convolution of the delta function with any other tempered distribution S is simply S: S*\delta = S.\, That is to say that δ is an identity element for the convolution on tempered distributions, and in fact the space of compactly supported distributions under convolution is an associative algebra with identity the delta function.

For example, the C. albicans tRNACAGSer contains identity elements for the LeuRS, namely m1G37 and the middle base of the anticodon (A35), but the discriminator base at position 73 (G73) is specific for SerRS and not for LeuRS (A73 discriminator) [62].

Studies on the tRNAThr identity elements for two Archaea species revealed that their discriminator base and acceptor stem base pairs are used differently.

In contrast to other E. coli tRNAs, the identity elements for recognition of the proly tRNAs by the E. coli prolyl-tRNA synthetase (C1, G72, and A73) are similar to those in tRNA CUA MjTyr.

In other words, coevolution of bacterial GlnRS-tRNAGln is phylum-specific or divergent, and, the experimentally determined tRNAGln identity elements for a bacterium in one phylum (γ-protobacteria) may not strictly hold true for another bacterium belonging to a different phylum (deinococcus-thermus).

The identity element of a system or group of numbers (for a particular operation) always yields the original number itself (its identity).